6.  3D computer graphics studies at ESSI

Jean-Claude Lafon, Peter Sander and Michel Buffa

Abstract

In this paper we present the teaching of three-dimensional computer graphics at ESSI: focusing on the students and their aims, the objectives and structure of the courses, the way they are taught and the problems that have been experienced.

Who is being taught?

In the ESSI engineering school, solid modelling is taught to computer science students who are four and five years past their baccalaureat. These students are aiming to find jobs in high-technology industries, for instance:

• The computer industry: DEC, IBM, Texas instruments etc. A number of our students go into the manufacture of VLSI circuits.
• The aerospace industry: Aerospatiale, Dassault Aviation and Eurocopter etc.
• Military industries including Thomson and DCL Toulon.
• The pharmaceutical industry: companies such as Cordis and Wellcome.
• Many others, such as Télémécanique, Air France, Franlab etc.

All the students starting to learn about solid modelling can be expected to have a good knowledge of the principles of computer science, and in particular of:

• Computer architectures.
• The Unix operating system and X-Windows.
• Data-structures.
• The design and analysis of algorithms.
• Database technology.
• The methodology of object-oriented programming.
• Good programming practice in the C and  languages.

Objectives

The objectives of the course are to give students:

• A broad knowledge of today's 3D computer graphics.
• Practical experience in the development of computer graphics programs.
• The ability to make an immediate and effective contribution to an industrial project.

Equipment

The courses are taught on a network of 160 Sun SPARC workstations; ten SGI Indy workstations are also available. The software used includes Phigs, Pex, Renderware and POV, Open-GL and VRML (1.0 and 2.0).

Second-year course: 2D graphics

The second-year course covers the following topics:

• Spaces and transformations: world space, normalized device coordinates and screen space.
• Two-dimensional transformations.
• Image data-structures.
• Generation of lines (Bresenham's algorithm) and curves (Bézier curves and B-splines).
• Two-dimensional geometrical algorithms.
• Electronic publishing, inclusing programming in Postscript.
• Developing GUIs using Motif.

Example project

Figure 1. User interface for the design of a furnished flat.

A typical second-year project is the interactive design of a furnished flat, as shown in Figure 1. This is a one-week project that is undertaken by a class of about eighty students. Aspects of interest include enforcing object adjacencies and resolving constraints between objects, and the design of a data structure and a user interface.

Final-year course: 3D modelling and realistic rendering

The final-year course on modelling and rendering covers the following topics:

• Homogeneous coordinates; three-dimensional transformations; space curves and surfaces.
• Models: wire-frame, surface, solid (B-rep and CSG) models and functional.
• Visualization: perspective, hidden-surface algorithms, lighting, texture, transparency and ray-tracing.
• CAD applications: methodology, databases, parameterized objects, data exchange (especially SET), the use of constraints and AI techniques in CAD.
• Programming in PHIGS.

We teach PHIGS because it is an ISO/IEC standard widely used in French industry. Coordinate systems and clipping are very well described; hierarchical modelling is possible with the use of structures; and the viewing model is very clear in PHIGS. There is also the concept of workstation, appearance control and logical input devices and interaction models, although these are not so relevant to 3D work. However OpenGL will be used in future as it is more attractive on SGI machines.

Both the second-year and final-year courses have the same form:

• 20 hours of theoretical lectures.
• Individual exercises of increasing difficulty, with some staff support provided.
• A collective small project (2-3 students working together for 40 hours).
• A final project running over two days per week for five months (for groups of two to four students). Not all students do a final project in 3D graphics, however.

Typical exercises include:

• Visualization of surfaces with hidden lines removed.
• Interactive design of simple surfaces (revolutes and extrusions). An example is shown in Figure 2.

Figure 2. A "small 3D modeller".

Small projects

Small Project 1: modelling and animation of cranes

Figure 3. Several tower cranes modelled in PHIGS.

A tower crane is in fact a rather complex structure, composed of many different sub-assemblies: rail, tower, top-of-tower, cab, carriage. The hierarchical structures of PHIGS is very convenient for the modelling of such structures. Each component of the crane is defined in its own coordinate system and approximated by a rectangular parallelpiped. In this projects, the students use PHIGS to learn about:

• The PHIGS structure hierarchy and structures operators.
• Local and global modelling transformations.
• Structure editing.

Cranes are also moving objects (moving parts include the base on rails, the tower, the jib, the wagon and the load itself). The motion is described in a Cartesian coordinate frame, in which the relative positions and orientations of objects are represented by homogeneous transformations between coordinate systems attached to each component, and combined by matrix multiplications. Matrices are convenient for expressing consecutive transformations, and fit well with the viewing pipeline of PHIGS which is used in its implementation.

To visualize the cranes that they have modelled, the students have to define the position of the camera and the type of projection to be used. So they need to study the viewing pipeline and the viewing model in PHIGS, the different parallel and perspective projections, and the different PHIGS attributes. An example picture is shown in Figure 3.

A major aim of this project is to show the student the importance of program portability (this is a reason for using PHIGS). For compatibility reasons we cannot produce shaded pictures from PHIGS+, but we can transfer the models to POV for this purpose.

The students have achieved good results in this exercise, and employed good programming practice ... which was our main objective.

Small project 2: Interactive three-dimensional design of a furnished flat

Figure 4. A furnished kitchen.

This is an extension of the (2D) second-year project on designing a flat. In this project, modelling is more complex. The resulting models can be rendered with Pex or POV (see Figure 4).

Final projects

Final project 1: Modelling and animation of a robot

This project was done by two students working together. They use an object-oriented approach to describe the direct and inverse kinematics of robots. The results of this project have themselves been used for teaching about robot manipulation

Final project 2: Declarative modelling of polyhedra

This was another project undertaken by a pair of students. The aim was to be able to define classical convex or non-convex polyhedra, and to render them using POV. This was a challenging project, especially because the usuall books on this subject (e.g. Berge, Coxeter) are too difficult for computer science students.

Final project 3: Putting an interactive walkthrough of the ESSI building on to the World Wide Web

Figure 5. The exterior view of the ESSI building that is on the Web.

Figure 6. The interior view of the ESSI building that is on the Web.

This was a four-student project. The main aims were to explore the field of VR; to use AutoCAD to model the buildings (This would have been too difficult using PHIGS or OpenGL); to use VRML to construct the virtual walkthrough. It was also a multimedia project; if you click on to a specific desk, a teacher will appear and speak.... (See Figures 5 and 6, or http://www.essi.fr/~sander/proj/EssiVR.

Other final year projects included:

• Three-dimensional oilfield visualization with PHIGS.
• Using the Voronoi diagram to discretize an oilfield (see Figure 14).
• Computation of isosurfaces.

Conclusions

Our approach gives good results with our students, but we have some difficulties:

• It is difficult to estimate the time necessary for students to complete a project (and the time is limited).
• Books on these topics are good (often excellent) for theory, but not so suitable for software developers (see references).
• Existing modellers seem to be too complicated for student use, or they are too expensive, or both.

We are searching for now software tools, such as a suitable 3D modeller and an object-oriented graphics language, and of course we always need new ideas for practical projects.

References

Theoretical books (to support lectures):

1. J.D. Foley, A. Van Dam et al., Fundamentals of Interactive Computer Graphics, 2nd. ed., Addison-Wesley, 1990.
2. C.M. Hoffmann, Geometric and Solid Modeling: an Introduction, Morgan Kaufman, 1989.
3. M.A. Mäntylä, Introduction to Solid Modeling, Computer Science Press, 1988.
4. P. Schweizer, Infographie, Vols. I and II, Presses Polytechniques Romandes, 1987.
5. A. Watt and M. Watt, Advanced Animation and Rendering Techniques, Addison-Wesley, 1992.
6. J.R. Woodwark, Calcul de Formes par Ordinateur, Masson, 1988.

Technical books (to support projects):

1. A.L. Ames, D.R. Nadeau and J.L. Moreland, The VRML Sourcebook, Wiley, 1996.
2. T. Berlage, OSF/MOTIF—Concepts and Programming, Addison-Wesley 1991.
3. T. Gaskins, Pexlib Programing Manual, O'Reilly, 1992.
4. J. Neider, T. Davis and M. Woo, OpenGL Programming Guide, Addison-Wesley, 1990.

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